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4 ideas
| 9998 | What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber] |
| Full Idea: There are three different uses of the number words: the singular-term use (as in 'the number of moons of Jupiter is four'), the adjectival (or determiner) use (as in 'Jupiter has four moons'), and the symbolic use (as in '4'). How are they related? | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §1) | |
| A reaction: A classic philosophy of language approach to the problem - try to give the truth-conditions for all three types. The main problem is that the first one implies that numbers are objects, whereas the others do not. Why did Frege give priority to the first? |
| 10002 | '2 + 2 = 4' can be read as either singular or plural [Hofweber] |
| Full Idea: There are two ways to read to read '2 + 2 = 4', as singular ('two and two is four'), and as plural ('two and two are four'). | |
| From: Thomas Hofweber (Number Determiners, Numbers, Arithmetic [2005], §4.1) | |
| A reaction: Hofweber doesn't notice that this phenomenon occurs elsewhere in English. 'The team is playing well', or 'the team are splitting up'; it simply depends whether you are holding the group in though as an entity, or as individuals. Important for numbers. |
| 12488 | The idea of 'one' is the simplest, most obvious and most widespread idea [Locke] |
| Full Idea: Among all the ideas we have, as there is none suggested to the mind by more ways, so there is none more simple than that of unity, or one; ..every idea in our understanding, every thought of our minds brings this idea along with it. | |
| From: John Locke (Essay Conc Human Understanding (2nd Ed) [1694], 2.16.01) | |
| A reaction: What does Locke mean by 'suggested' to the mind? I take it that this phenomenon of psychology (or of reality, if you like) is the foundation of mathematics, making one clearly prior to zero. |
| 12489 | If there were real infinities, you could add two together, which is ridiculous [Locke] |
| Full Idea: If a man had a positive idea of infinite, either duration or space, he could add two infinities together; nay, make one Infinite infinity bigger than another, absurdities too gross to be confuted. | |
| From: John Locke (Essay Conc Human Understanding (2nd Ed) [1694], 2.17.20) | |
| A reaction: A beautifully heartfelt objection to everything Cantor stood for, two hundred years before Cantor got round to it. |